GEOMETRIC CONSTRUCTION OF ASSOCIATION SCHEMES FROM DEGENERATE QUADRICS INPROJECTIVE SPACES PG(2v+δ+l-1,Fq) FOR q ODD

Let Fq be a finite field with q elements,where q is a power of an odd prime.In this paper,the authors consider a projective space PG(2v+δ+l,Fq) with dimension 2v+δ+l,partitioned into an affine space AG(2v+δ+l,Fq) of dimension 2v+δ+l and a hyperplane H=PG(2v+δ+l-1,Fq) of dimension 2v+δ+l-1 at infinity,where l≠0.The points of the hyperplane Hare next partitioned into four subsets.A pair of points a and b of the affine space is defined to belong to class i if the line ab meets the subset i of H.Finally,a family of four-class association schemes are constructed,and parameters are also computed.